AN ELEMENTARY APPROACH TO WEIGHT MULTIPLICITIES IN BIVARIATE IRREDUCIBLE REPRESENTATIONS OF Sp(2r)

作者：Maddox Julia^*

来源：Communications in Algebra, 2014, 42(9): 4094-4101.

DOI：10.1080/00927872.2013.804928

• Multilinear algebra
• Standard representation
• Symmetric tensor
• Symplectic Lie algebra
• Symplectic Lie group
• Weight multiplicity
• 17B10
• 05E10

By bivariate irreducible representations of Sp(2r), we mean irreducible representations with highest weights containing at most two nonzero entries, using the usual identification of dominant weights for complex symplectic Lie algebras and their corresponding Lie groups as r-tuples in decreasing non-negative integers. This paper has two aims. The first aim is to provide a formula for the weight multiplicities of said representations, which is easily computable. The second aim is to present these weight multiplicities using elementary means. The formula for these weight multiplicities is derived using basic multiliear algebra and combinatorial arguments through explicit descriptions of weight vectors.

• 出版日期2014-9-2